In this paper, we deal with compact operators on a Hilbert space, within the framework of Bishop's constructive mathematics. We characterize the compactness of a bounded linear mapping of a Hilbert space into C n , and prove the theorems: Let A and B be compact operators on a Hilbert space H , let C be an operator on H and let α ϵ C . Then α A is compact, A + B is compact, A ∗ is compact, CA (...) is compact and if C ∗ exists, then AC is compact; An operator on a Hilbert space has an adjoint if and only if it is weakly compact. (shrink)

We show, within the framework of Bishop's constructive mathematics, that (sequential) completeness of the locally convex space $\mathcal{D} (\mathbb{R})$ of test functions is equivalent to the principle BD-N which holds in classical mathemtatics, Brouwer's intuitionism and Markov's constructive recursive mathematics, but does not hold in Bishop's constructivism.

We deal with a restricted form WC-N' of the weak continuity principle, a version BT' of Baire's theorem, and a boundedness principle BD-N. We show, in the spirit of constructive reverse mathematics, that WC-N'. BT' + ¬LPO and BD-N + ¬LPO are equivalent in a constructive system, where LPO is the limited principle of omniscience.

We introduce Kripke models for propositional substructural logics with strong negation, and show the completeness theorems for these logics using an extended Ishihara's canonical model construction method. The framework presented can deal with a broad range of substructural logics with strong negation, including a modified version of Nelson's logic N$^-$, Wansing's logic COSPL, and extended versions of Visser's basic propositional logic, positive relevant logics, Corsi's logics and M\'endez's logics.

Ishiharaʼs boundedness principleBD-N was introduced in Ishihara [5] and has turned out to be most useful for constructive analysis, see e.g. Ishihara [6]. It is equivalent to the statement that every sequentially continuous function from NN to N is continuous w.r.t. the usual metric topology on NN. We construct models for higher order arithmetic and intuitionistic set theory in which both every function from NN to N is sequentially continuous and in which the axiom of choice from NN (...) to N holds. Since the latter is known to be inconsistent with the statement that all functions from NN to N are continuous these models refute BD-N. (shrink)

The article analyzes literature addressing the problem of reality in modern anti-realist theories. The purpose of the review is to expand the circle of researchers, including not only representatives of analytical philosophy, but also those of the phenomenological tradition, since the principle of phenomenological reduction corresponds to the general conceptual attitude of anti-realists, and in methodological terms, phenomenology more consistently implements the program of anti-realism. The principle of anti-realist philosophy is shown as exemplified in solutions of the “difficult problem of (...) consciousness” within analytical philosophy and also in the development of a phenomenological attitude. Such a combination of two, by far the most respectable, philosophical schools makes it possible to more accurately determine the contribution of theorists of both directions to the theory of reality, to identify problematic nodes, internal disagreements and points of intersection of the ideas of phenomenologists and representatives of analytical philosophy in understanding the nature of reality. The works of modern researchers of the problems of reality R. Berghofer, V. Vasyukov, Ya. Ishihara, V. Ladov, L. Makeeva, R. Pils, A. Fursov, D. Chalmers and many others, as well as the works of E. Husserl, W. Quine, H. Putnam’s works, which have become philosophical classics, allow us to clarify the ideas about reality that have developed in the anti-realist discourse from different sides. New studies of the principle of phenomenological reduction by Yu. Himanka and the origins of the formation of phenomenological philosophy by N.V. Motroshilova make it possible to clarify the contribution of phenomenologists to the anti-realist tradition. (shrink)

In the informal setting of Bishop-style constructive reverse mathematics we discuss the connection between the antithesis of Specker’s theorem, Ishihara’s principle BD-N, and various types of equicontinuity. In particular, we prove that the implication from pointwise equicontinuity to uniform sequential equicontinuity is equivalent to the antithesis of Specker’s theorem; and that, for a family of functions on a separable metric space, the implication from uniform sequential equicontinuity to uniform equicontinuity is equivalent to BD-N.

The notions of permutable and weak-permutable convergence of a series|$\sum _{n=1}^{\infty }a_{n}$|of real numbers are introduced. Classically, these two notions are equivalent, and, by Riemann’s two main theorems on the convergence of series, a convergent series is permutably convergent if and only if it is absolutely convergent. Working within Bishop-style constructive mathematics, we prove that Ishihara’s principle BD-|$\mathbb {N}$|implies that every permutably convergent series is absolutely convergent. Since there are models of constructive mathematics in which the Riemann permutation theorem (...) for series holds but BD-|$\mathbb{N}$|does not, the best we can hope for as a partial converse to our first theorem is that the absolute convergence of series with a permutability property classically equivalent to that of Riemann implies BD-|$\mathbb {N}$|. We show that this is the case when the property is weak-permutable convergence. (shrink)

Aims: To review the literature on perceptions of nursing students and/or educators on the contribution of ethics education to ethical competence in nursing students. Background: Nurses do not always demonstrate the competencies necessary to engage in ethical practice. Educators continue to debate about the best ways to teach ethics to nurses so that they can develop ethical competencies. Data sources: MEDLINE, Embase, CINAHL, PsycINFO, and Web of Science. Review methods: A total of 15 articles with a quantitative, qualitative, or mixed-methods (...) design published between January 1992 and March 2012 were analyzed. Results: According to students and educators, ethics education increases ethical perception of nursing students and the development of reflective and analytical skills. However, its contribution to the development of ethical behavior was barely mentioned. The accounts of students and educators revealed essential features of effective ethics education: active involvement of students in case study discussions and use of ethical frameworks. The use of activating educational strategies requires a safe learning environment where students can openly reflect on values at stake in their care practice. Conclusion: A better understanding of how students learn to develop ethical skills and of influencing factors can guide educators to develop ethics courses for nursing curriculum. Future research needs to focus on the methodological accuracy of sampling and measuring instruments. (shrink)

Courts and jurors sometimes refuse to assign liability to defendants on the basis of statistics alone, despite their apparent reliability. I argue that this refusal is best understood as a recognition of defendants’ right to security. Understood as a robust good in Philip Pettit’s sense, security requires that someone risking harm to others’ protected interests adopt a disposition of concern that controls against wrongfully harming them. Since trials risk harm, the state must adopt such a disposition. Statistics leave open the (...) possibility of innocence and so wrongful harm in a way that the state cannot ignore; if it does use such statistics, it makes defendants wrongfully insecure. This explanation of the problem of bare statistical evidence is especially apt because security grounds the right to a fair trial and judicial procedural rights more generally. (shrink)

The purpose of the present study was to examine whether or not strong values might influence physicians' estimations of future events. In an empirical study about physicians' attitudes towards physician assisted suicide (PAS) we asked about the physicians' main reasons for being pro, doubtful or contra PAS and also asked them to estimate what would happen with patients' trust if PAS were to be legally accepted in Swedish society. Finally we asked the physicians about their own trust in healthcare in (...) the event of PAS being legally accepted. We found that in contrast to those who were pro PAS and doubtful, the group who were against PAS did not discriminate between their own opinion and their estimation of what they thought might happen with patients' trust in the future. Against the backdrop of the present study, we present a hypothesis maintaining that feeling strongly against controversial medical procedures is associated with being inclined to let one's own beliefs influence our capacity to interpret and estimate empirical results. We think this hypothesis merits closer examination. (shrink)

The theory of branching space-times, put forward by Belnap, considers indeterminism as local in space and time. In the axiomatic foundations of that theory, so-called choice points mark the points at which the possible future can turn out in different ways. Working under the assumption of choice points is suitable for many applications, but has an unwelcome topological consequence that makes it difficult to employ branching space-times to represent a range of possible physical space-times. Therefore it is interesting to develop (...) a branching space-times theory without choice points. This is what we set out to do in this paper, providing new foundations for branching space-times in terms of choice sets rather than choice points. After motivating and developing the resulting theory in formal detail, we show that it is possible to translate structures of one style into structures of the other style and vice versa. This result shows that the underlying idea of indeterminism as the branching of spatio-temporal histories is robust with respect to different implementations, making a choice between them a matter of expediency rather than of principle. (shrink)

Disturbing international inequalities in health abound. Life expectancy in Swaziland is half that in Japan. A child unfortunate enough to be born in Angola has 73 times as great a chance of dying before age 5 as a child born in Norway. A mother giving birth in southern sub-Saharan Africa has 100 times as great a chance of dying from her labor as one birthing in an industrialized country. For every mile one travels outward toward the Maryland suburbs from downtown (...) Washington, DC on its underground rail system, life expectancy rises by a year – reflecting the race and class inequities in American health. Are the glaring, even larger, international health inequalities also unjust? -/- All of us no doubt think they are grossly unfortunate. Many of us think they are unfair or unjust. Why should some people be at such a health disadvantage through no fault of their own, losers in a natural and social lottery assigning them birth in an unhealthy place? Others of us are troubled by the absence of the kinds of human relationships that ordinarily give rise to the claims of egalitarian justice that we make on each other – for example, being fellow citizens or even interacting in a cooperative scheme. Who has obligations of justice to reduce these international inequalities? And do those obligations hold regardless of how the inequalities came about? What institutions are accountable for addressing them? (shrink)

Decisions about targeting medical assistance in humanitarian contexts are fraught with dilemmas ranging from non-availability of basic services, to massive demographic and epidemiological shifts, and to the threat of insecurity and evacuations. Aid agencies are obliged, due to capacity constraints and competing priorities, to clearly define the objectives and the beneficiaries of their actions. That aid agencies have to set limits to their actions is not controversial, but the process of defining the limits raises ethical questions. In MSF, frameworks for (...) resource allocation are subject to constant reflection and reiteration, and perspectives are sought at all levels, from implementers at the programme level to the operational directors at headquarters. The perspectives of the programmes staff hold considerable weight as they have the knowledge and experience with particular communities to assess the degree of vulnerability and need, and are also the people who ultimately have to give explanations to beneficiaries when changes or closures are going to be instituted. Humanitarian agencies have a responsibility to ensuring that their workers are prepared to reflect on these dilemmas, and challenge the status quo when it costs lives. (shrink)

Christianity has been crucial in the conceptualization and articulation of the moral framework of the Western tradition. The social sciences, including ethics, were modeled on physical science. However, the Enlightenment project inculcated a metaphysics and an epistemology that reduced the subject to an object and thus undermined the conditions of freedom, agency and an accessible cosmic order; all of which are essential to morality. Competing value claims were shunted into a political context for resolution, but the politicalized morality itself requires (...) a framework for evaluating resolutions. While neither the Enlightenment nor post-modernism can provide such a framework, Christian tradition can, in fact, provide just such a framework and response. (shrink)